Model Selection of Kernel Ridge Regression for Extrapolation

Model selection of the kernel ridge regression is discussed in this paper. The cross-validation approach is one of popular and powerful model selection techniques for many machine learning methods including the kernel ridge regression. However, the cross-validation approach is not suitable for extrapolation scenarios due to its principle. In this paper, we propose a novel model selection criterion for the kernel ridge regression which is applicable to extrapolation scenarios. The key idea of the proposed criterion is direct evaluation of the generalization error, defined in a certain reproducing kernel Hilbert spaces, which is feasible under a certain assumption on a set of kernel candidates.